Rewrite the expression in the form $k\cdot y^n$. $\left(4\sqrt[4]{y^5}\right)^{^{\scriptsize\dfrac12}}=$
$\begin{aligned} \left(4\sqrt[4]{y^5}\right)^{^{\scriptsize\dfrac12}}&=\left(4y^{^{\scriptsize\dfrac54}}\right)^{^{\scriptsize\dfrac12}} \\\\ &=4^{^{\scriptsize\dfrac12}}y^{^{\scriptsize\dfrac54\cdot\dfrac12}} \\\\ &=2y^{^{\scriptsize\dfrac58}} \end{aligned}$